Back to Algebraic Geometry Seminar: Fall 2022
Algebraic Geometry Seminar
Date: Tuesday, Sep 20, 2022
Time: 3:30PM - 4:30PM
Location: LCB 323
Lei Wu
KU Leuven
Title |
Logarithmic cotangent bundles, Chern classes, and applications |
Abstract |
Using MacPherson’s Euler obstruction function, one can identify the abelian group of constructible functions with the group of algebraic cycles on a smooth complex algebraic variety. Kashiwara’s local index formula gives an alternative approach to this identification by using characteristic cycles for holonomic D-modules (they are Lagrangian cycles in the cotangent bundle). This identification then enables us to define Chern classes of algebraic cycles by using characteristic cycles. In this talk, I will first explain how to obtain Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement by using logarithmic cotangent bundles motivated by D-module theory. Then I will discuss applylications of such Chern classes in understanding Chern-Mather classes of very affine varieties and in proving the Involution Conjecture of Huh and Sturmfels in likelihood geometry. This work is joint with Maxim, Rodriguez, and Wang. |
Algebraic Geometry